Article comprising a Bragg grating in a few-moded optical waveguide

ABSTRACT

Disclosed is an article that comprises an optical waveguide mode converter for converting light of wavelength λ in a few-moded optical waveguide from a given guided mode (e.g., LP 01,f ) to another guided mode (e.g., LP 02,b ). The converter comprises a tilted refractive index grating in the core of the waveguide. Appropriate choice of the refractive index profile n(r), photosensitivity p(r) and tilt angle θ makes possible substantial nulling of the coupling between some guided modes (e.g., LP 01,f  to LP 01,b  and LP 01,f  to LP 11,b ), and substantial maximization of the coupling between other guided modes (e.g., LP 01,f  to LP 02,b ). Mode converters according to the invention can be advantageously used in optical fiber communication systems in add/drop multiplexers.

RELATED APPLICATIONS

This application is related to concurrently filed U.S. patentapplication Ser. No. 09/584,071 by T. A. Strasser et al., titled“Article Comprising a Tilted Grating in a Single Mode Waveguide”, filedMay 31, 2000, incorporated herein by reference.

FIELD OF THE INVENTION

This application pertains to few-moded optical waveguides with arefractive index (Bragg) grating, and to optical communication systemsthat comprise such waveguides.

BACKGROUND

Bragg gratings (also referred to as refractive index gratings) inoptical waveguides are known. Conventionally such gratings couple aforward-propagating core-guided mode in single mode fiber to thebackreflected core mode.

Mode conversion gratings are also known. See, for instance, U.S. Pat.Nos. 5,717,798 and 5,740,292. The latter discloses reflective gratingsthat inter alia couple light in the fundamental mode (LP₀₁) to the LP₁₁mode.

Mode coupling gratings can find a variety of uses in optical waveguidesystems. For instance, they can serve as wavelength routing filters inWDM networks.

However, it has been found that reflective grating mode converters thatefficiently convert LP₀₁ radiation to LP₁₁ radiation frequently aredifficult to manufacture, due to the spatial degeneracy of the LP₁₁mode. Whereas one of the LP₁₁spatial modes typically can be converted toLP₀₁ by a LP₀₁ to LP₁₁ mode converter, the other LP₁₁ spatial modetypically can not be so converted, due to the interference of two nearbydegenerate spatial modes. This spatial degree of freedom is difficult tocontrol. Thus, it would be desirable to have available a mode converterwhich does not involve coupling to or from a spatially degenerate mode.

In particular, there is a need for a mode converter which couples theLP₀₁ mode to the LP₀₂ mode, without coupling the LP₀₁ mode to any otherguided mode, e.g., LP₁₁ and reflected LP₀₁. Such an LP₀₁-LP₀₂ modeconverter could be used, for instance, in an add/drop multiplexer. Thiswould avoid the need for an expensive and lossy circulator. Circulatorsare essential in implementing prior art Bragg grating-based add/dropfiltering applications.

The LP₀₂ mode is not spatially degenerate and thus can be efficientlyconverted to LP₀₁. However, a LP₀₁ to LP₀₂ mode converting reflectivegrating typically must be designed such that both the LP₀₁ to LP₁₁ modeconversion and the LP₀₁ to LP₀₁ mode conversion are substantiallynulled. The LP₁₁ mode must exist in the optical fiber since, in orderfor the LP₀₁ to LP₀₂ mode conversion to be strong, the optical fibermust guide the LP₀₂ mode, and therefore must also guide the LP₁₁ mode.To the best of our knowledge, the prior art does not provide a techniquefor making such a reflective LP₀₁ to LP₀₂ mode converter. Thisapplication inter alia discloses such a mode converter.

C. X. Shi, IEEE Journal of Quantum Electronics, Vol. 32(8), August,1996, page 1360, provides a theoretical treatment of a fiber-opticFabry-Perot resonator with two mode conversion (LP₀₁ to LP₀₂) “mirrors”.See also C. X. Shi et al., Optics Letters, Vol. 17(23), page 1655,December 1992; and F. Bilodeau et al., Electronics Letters, Vol. 27(8),page 682, April 1991.

M. J. Holmes et al., ECOC '99, Sep. 26-30, 1999, Nice, France, pagesI-216-217 disclose a fiber for sidetap filters. The fiber had anon-photosensitive core dopant for normalized radius less than 0.4, acombination of a non-photosensitive core dopant and germania fornormalized radius 0.4-1, and a photosensitive cladding doped withgermania out to a normalized radius of 3.5, to which boron was added toreduce the cladding index to match the deposition tube. The germaniaconcentrations for the regions 0.4-1.0 and 1.0-3.5 were in the ratio0.6:1.0 in order to obtain the required relative photosensitivity. TheHolmes et al. paper thus discloses fiber in which the core had twodifferent photosensitivity levels, with the cladding also beingphotosensitive. The photosensitivity profile was chosen to optimize thewavelength dependence of the cladding mode loss spectrum forapplications, and not to obtain a mode converter of the herein relevanttype.

All cited references are incorporated herein by reference.

GLOSSARY AND DEFINITIONS

For ease of exposition the discussion herein will generally refer tooptical fibers. It will be appreciated, however, that similar resultsare obtainable in other optical waveguides, e.g., in planar waveguides.

The “coupling strength” between two guided core modes in a few-modedoptical fiber is conventionally expressed in terms of an overlapintegral, as shown in equation 2) below. The coupling strength typicallydepends on the refractive index profile n(r), the photosensitivityprofile p(r), and the tilt angle θ.

“Minimizing” the coupling between two guided core modes in a givenwaveguide means adjusting the tilt angle of a tilted grating such thatthe coupling strength between the two modes is less than −30 dB.

“Maximizing” the coupling between two guided core modes in a givenwaveguide means adjusting the tilt angle of a tilted grating such thatthe coupling strength between the two modes is at least about −10 dB.

By a “regular null” we mean herein a tilt angle region in a tilted(“blazed”) fiber Bragg grating that has a core mode coupling strengthfor light of a predetermined wavelength that is less than −30 dB overonly a small (typically less than 0.1°) angular range of the tilt angle.Regular nulls occur for many tilt angles.

By a “super null” we mean two (or possibly more) regular nulls thatoccur at closely spaced tilt angles, thereby making the core modecoupling at the predetermined wavelength very low (typically less than−30 dB) over a relatively large (more than 0.1°, desirably more than0.2°, or even 0.5° or more) range of tilt angles between the regularnulls.

Modes of the guided light are designated LP_(mn) in conventionalfashion, with m and n being integers. Por instance, LP₀₁ is thefundamental mode. LP_(01,f) refers to the forward propagatingfundamental mode, and LP_(01,b) refers to the backward propagatingfundamental mode.

“Photosensitivity” refers to the refractive index change in thewaveguide that results if an appropriately doped waveguide is exposed toactinic radiation, typically UV radiation.

A “few-moded” optical waveguide supports the fundamental mode and one ormore higher order modes, typically no more than about 10 guided modestotal.

The description of the invention herein is generally in terms ofconversion between the fundamental mode and a higher order mode such asLP₀₂. This is for the sake of concreteness only, and the invention atleast in principle can be embodied in an article for mode conversionbetween two appropriate higher order modes.

SUMMARY OF THE INVENTION

In an exemplary mode converter according to the invention, it isnecessary that LP_(01,f) light be strongly coupled into the LP_(02,b)mode. However, in such a mode converter the coupling between LP_(01,f)and all other guided reflected modes (exemplarily LP_(11,b) andLP_(01,b)) has to be small, exemplarily at least 20 dB less thanLP_(01,f) to LP_(02,b) coupling. This simultaneous “nulling” of thecoupling between LP_(01,f) and the other guided modes (i.e., other thanthe desired coupling) can not be achieved with optical fiber that hasuniform photosensitivity throughout the core, necessitating use of amore complex fiber design, as is described below.

The coupling strengths between the various guided modes in an opticalfiber depend on the refractive index profile of the fiber and theelectric fields of the various modes. Both of these parameters generallyare fixed at the time of grating formation, and thus can not be variedto achieve a desired coupling. The only grating parameter which can bechanged to significantly alter the relative coupling strengths is thetilt of the grating with respect to the core axis. However, with uniformphotosensitivity in the fiber core, the control over the variouscoupling strengths that is achievable by introduction of a tilt in thegrating is limited. In particular, with a uniform radialphotosensitivity profile, it is impossible to “null” simultaneously aneven-even reflection (e.g., LP_(01,f) to LP_(01,b)) and an even-oddreflection (eg., LP_(01,f) to LP_(11,b)). Thus, we have determined thatan additional degree of freedom has to be provided. This degree offreedom is the photosensitivity profile of the optical fiber. Thisprofile has at least two distinct levels of photosensitivity in the core(of which one or more can be zero), and may, but need not, havesubstantially no photosensitivity in the cladding.

Thus, by way of example, forming a Bragg grating in an optical fiberwherein photosensitivity is removed (or substantially reduced) incertain regions of the fiber core makes it possible to achieve a muchbroader range of relative coupling strength as a function of the tiltangle of the fiber than is possible with fiber having uniformphotosensitivity in the core. In particular, it is possible tosimultaneously null both an even-even (e.g., LP_(01,f) to LP_(01,b)) andan even-odd (e.g., LP_(01,f) to LP_(11,b)) reflection, with strongLP_(01,f) to LP_(02,b) coupling, something that is not possible with atilted refractive index grating that has uniform photosensitivity in thecore.

More generally, the invention is embodied in an article that comprisesan optical waveguide mode converter for converting light of wavelength λ(exemplarily about 1.5 μm) from a forward-propagating given guided modeto another predetermined guided mode. The mode converter comprises atilted refractive index grating in the waveguide, the grating having atilt angle θ with respect to the waveguide axis and extendinglongitudinally over at least a portion of the waveguide. The waveguideis a few-moded waveguide for light of wavelength λ and has a core and acladding that contactingly surrounds the core. The fiber has a dopantdistribution selected to provide the fiber with a refractive indexprofile n(r) and a photosensitivity profile p(r), with both profilesbeing functions of the radial coordinate r of the waveguide.

The mode converter has two or more non-zero coupling strengths amongcore guided modes, and p(r) has at least two different levels ofphotosensitivity in the core. Furthermore, n(r), p(r) and θ are selectedsuch that more than one of said non-zero coupling strengths aresimultaneously nulled. For instance, n(r), p(r) and θ are selected suchthat a given guided mode (e.g., LP_(01,f)) is nulled with at least oneother guided mode (e.g., LP_(01,b) and LP_(11,b)), and is stronglycoupled to at least one other guided mode (e.g., LP_(02,b)). In apreferred embodiment of the invention, the fundamental mode LP_(01,f) isnulled simultaneously with an even and an odd backward-propagatingguided mode (LP_(01,b), and LP_(11,b), respectively), and LP_(01,f) issimultaneously strongly coupled to a higher order even mode (e.g.,LP_(02,b)).

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1a and 1 b schematically show a refractive index profile and aphotosensitivity profile for an exemplary fiber according to theinvention;

FIGS. 2a-2 c schematically show the index profile, photosensitivityprofile and mode electric fields of a fiber according to the invention;

FIG. 3 shows various coupling constants as a function of tilt angle;

FIGS. 4a-4 b schematically depict an exemplary photosensitivity profileand refractive index profile, respectively; and

FIG. 5 schematically shows an optical fiber communication systemcomprising a mode converter according to the invention.

DETAILED DESCRIPTION

Below we provide mathematical expressions that can be used to determinea photosensitivity profile that at least approximately provides thedesired coupling strengths. If desired, optimized results can then beobtained by, typically minor, variation of the tilt angle, or possiblyof the photosensitivity profile. Trimming of the photosensitivityprofile by UV exposure can also be used for optimization.

The coupling between a first and a second guided mode (designatedLP_(mn) and LP_(pq)) in an optical waveguide depends on the couplingstrength κ, which is proportional to the following θ-dependent integral

κ_(mn-pq) (θ)=∫E_(mn)E_(pq) H(r)rdr,  1)

where H(r) depends on the mode indices and on the grating tilt angle(see, for instance, T. Erdogan et al., “Tilted Fiber Phase Gratings”, J.Optical Soc. America, A. Vol. 13(2), pages 296-313, 1996), incorporatedherein by reference.

For instance, if an optical fiber supports the LP₀₁ mode as well as theLP₁₁ mode then a tilted grating will couple the LP₀₁ mode to the LP₁₁mode with a strength that depends on the LP₀₁ to LP₁₁ overlap integral.That is to say:

κ₀₁₋₁₁ (θ)=∫E₀₁E₁₁J₁ (K_(grating)r sin θ) W(r)rdr,  2)

where E₀₁ and E₁₁ are the radially dependent electric field amplitude(normalized to unity, i.e., ∫₀ ^(∞)E² ₀₁ rdr=1) of the LP₀₁ and LP₁₁modes, K_(grating) is the wave vector of the grating(K_(gating)=2π/Δ_(grating)) θ is the tilt angle of the grating withrespect to the fiber axis, and W(r) is a radially dependent weightingfunction which expresses the radial variations of p(r), thephotosensitivity profile of the grating. The Bessel function J₁ arisesfrom the azimuthal integration and is zero when θ=0, since the LP₁₁ modeis odd and the LP₀₁ mode is even.

The weighting function W(r) can be defined via the full index modulationof the tilted grating, namely

δn(r,Φ,z)=δn W(r) exp[(iK_(grating))(sin θ r cos Φ+cos θz)].  3)

In equation 3, Φ is the azimuthal angle in cylindrical coordinates andδn is the amplitude of the index modulation. In a uniformlyphotosensitive fiber, W(r) is the same as the index profile n(r) and isunity up to the core radius. However, herein we consider fibers in whichW(r) is not uniform and may or may not have the same radial dependenceas the index profile n(r).

The above expressions can be used to determine the tilt angle θ thatyields the desired coupling between two given guided modes, for aselected photosensitivity profile. If the mathematically determinedvalue of θ does not directly yield the desired coupling strength then aminor amount of routine experimentation will typically suffice todetermine a corrected tilt angle that yields the desired coupling, e.g.,that nulls the coupling between the modes. After determination of thetilt angle that provides the desired coupling strengths, a gratinghaving the tilt angle and a desired length and strength is manufacturedin conventional manner.

In order to achieve efficient mode conversion between two predeterminedguided modes in a few-moded optical fiber it is typically necessary tosubstantially null all couplings except the mode conversion coupling,and substantially maximize the mode conversion coupling. By way ofexample, if the fiber supports LP₀₁, LP₁₁ and LP₀₂, and does not supportany other higher order modes (e.g., LP₂₁), and if the desired modeconversion is the LP_(01,f) to LP_(02,b) mode conversion, then theLP_(01,f) to LP_(01,b) coupling strength and the LP_(01,f) to LP_(11,b)coupling strength desirably are nulled, and the LP_(01,b) to LP_(02,b)coupling strength desirably is maximized.

For the sake of clarity the description below is for a LP₀₁ to LP₀₂ modeconverter in a three-moded optical fiber. The approach can be extendedto gratings in higher-moded optical fibers, and to coupling between anytwo spatial modes.

If a fiber supports an LP₀₁ and LP₁₁ mode then a tilted grating in thefiber will couple the LP_(01,f) mode to the LP_(11,b) mode with astrength that depends on the LP₀₁-LP₁₁ overlap integral. See equation 2above. Analogous statements can be made about LP_(01,f) to LP_(01,b)coupling and LP_(01,f) to LP_(02,b) coupling. By appropriate choice ofthe photosensitivity profile p(r) of the fiber it is possible tosimultaneously null the LP_(01,f) to LP_(01,b) coupling and theLP_(01,f) to LP_(11,b) coupling, and to obtain large LP_(01,f) toLP_(02,b) coupling.

In order to null both the LP₀₁ to LP₁₁ and the LP₀₁ to LP₀₁ couplings atthe same value of tilt angle θ, the photosensitivity profile p(r) mustbe appropriately selected. Simultaneous nulling is achieved when thephotosensitivity is removed (or substantially lowered) over a radialrange such that in the two coupling strength integrals the integrandsare both positive in one of the regions and both negative in the otherregion, and both cancel each other in the total integral. Alternately,the simultaneous LP₀₁ to LP₀₁ and LP₀₁ to LP₁₁ nulling can be understoodas the result of formation of a “supernull” for the LP₀₁-LP₀₁ couplingin which two regular nulls come close together for some value of tiltangle. This large angular range can then be made to overlap theLP₀₁-LP₁₁ angular null.

FIG. 1a schematically shows the refractive index profile of an exemplarythree-moded fiber according to the invention, and FIG. 1b schematicallyshows the photosensitivity profile of the fiber. In FIG. 1a, no refersto the refractive index of silica. The innermost core region 11 is dopedwith Ge and Al, making the region partly photosensitive. Theintermediate core region 12 is doped with Al, making itnon-photosensitive, and the outermost core region 13 is doped with Ge,making it strongly photosensitive. See FIG. 1b, wherein the three coreregions are designated 14-16, respectively.

FIGS. 2a-b schematically show the refractive index profile andphotosensitivity profile, and FIG. 2c shows the electric field strengthsof LP₀₁ (ref. numeral 21), LP₀₂ (ref. numeral 22) and LP₁₁ (ref. numeral23), respectively.

FIG. 3 shows the computed values of various coupling strengths as afunction of tilt angle, for the fiber of FIGS. 2a-c. As can readily beseen from FIG. 3, at θ˜6.5° the LP_(01,f) to LP_(01,b) coupling strength31 has a “super null”, and the LP_(01,f) to LP_(11,b) coupling strength32 has a regular null which overlaps the LP₀₁ to LP₀₁ supernull. At thesame tilt angle, the LP_(01,f) to LP_(02,b) coupling strength 33 hasvery nearly a maximum, thereby facilitating efficient mode conversion.

It will be appreciated that practice of the instant invention is notlimited to the photosensitivity profile specifically disclosed and isalso not limited to LP_(01,f) to LP_(02,b) mode converters. Few-modedoptical fibers are known and do not require further discussion.

Independent manipulation of the refractive index profile andphotosensitivity profile of a few-moded optical waveguide is not limitedto the above-described particular embodiment but can be applied in amore general design procedure to simultaneously null several higherorder mode couplings.

As an example of this general technique, the photosensitivity may be setat different levels p(r) in different annular regions 0 to r₁, r₁ to r₂,etc., as exemplified by FIG. 4a. The refractive index n(r) may likewisebe set at different values in a separate set of annular regions 0 to r₄,r₄-r₅, etc. The desired set of mode overlap integrals may then becalculated through a known mathematical optimization procedure. Theprocedure involves minimizing the unwanted couplings (and maximizing thedesired coupling strengths) as a function of the several variables thatdefine the fiber, namely the radii defining the photosensitivity andrefractive index profiles, the photosensitivity levels, the refractiveindex levels, and the tilt angle.

FIGS. 4a and 4 b schematically depict an exemplary photosensitivity andrefractive index profile of a few-mode fiber. The variables are p₁, p₂and p₃; r₁, r₂ . . . r₆; n₁, n₂ and n₃; and tilt angle θ. Theoptimization procedure involves evaluation of overlap integrals,substantially as shown above. The optimization procedure is directedtowards minimization (nulling) of predetermined coupling strengths(e.g., κ₀₁₋₀₁, κ₀₁₋₁₁, κ₀₁₋₀₂, κ₁₁₋₁₁ and κ₀₂₋₀₂), and maximizinganother predetermined coupling strength, e.g., κ₀₁₋₀₂. As anotherexample, in a three moded fiber, LP₀₁ is nulled with LP₀₂ and LP₁₁. Byway of further example, in a few-moded fiber (more than 3 guided modes)LP₀₁ is nulled with all guided modes except one, or LP₀₁ is nulled withall guided modes.

Mode converters as described above can find a variety of uses in anoptical fiber communication system. FIG. 5 schematically depicts anexemplary fiber optic communication system 50 wherein numeral 51 refersto a WDM transmitter, 52 refers to optical transmission fiber, 53 and 54refer to demultiplexers, and 55 to 57 light of wavelengths λ₁, λ₂ . . ., refer to receivers. Fiber 52 guides only the fundamental mode LP₀₁, tothe first de-multiplexer 53, which comprises a mode converter accordingto the invention. A channel (e.g., λ₁) is converted into LP₀₂, droppedfrom the signal stream and received by receiver 55. De-multiplexer 54similarly drops channel λ₂ which is detected by receiver 56. Otherchannels are dropped in similar manner, until only one channel (e.g.,λ_(n)) remains and is detected by receiver 57.

We claim:
 1. An article comprising an optical waveguide mode converterfor converting light of wavelength λ in a few-moded waveguide from agiven guided mode to another guided mode, the mode converter comprisinga tilted refractive index grating in the waveguide, the grating having atilt angle θ, the few-moded waveguide having a core and a claddingsurrounding the core, with the mode converter being associated amultiplicity of coupling strengths, wherein a) the few-moded waveguidehas a dopant distribution selected to provide the waveguide with arefractive index profile n(r) and a photosensitivity profile p(r),wherein n(r) and p(r) are functions of the radial coordinate of thewaveguide; b) p(r) has at least two different levels of photosensitivityin the core; and c) n(r), p(r) and θ are selected such that more thanone of said coupling strengths are simultaneously nulled, and such thatat least one of said coupling strengths is substantially maximized. 2.Article according to claim 1, wherein the few-moded waveguide is a3-moded waveguide, wherein said given guided mode is the fundamentalmode LP₀₁, and wherein n(r), p(r) and θ are selected such that a LP₀₁ toLP₁₁ coupling strength and a LP₀₁ to LP₀₂ coupling strength aresubstantially nulled, and such that a LP₀₁ to LP₀₁ coupling strength issubstantially maximized.
 3. Article according to claim 1, wherein saidgiven guided mode is the fundamental mode LP₀₁, and wherein n(r), p(r)and θ are selected such that the LP₀₁ coupling strength with all guidedmodes in the waveguide except one is nulled.
 4. Article according toclaim 1, wherein said given guided mode is the fundamental mode LP₀₁,and wherein n(r), p(r) and θ are selected such that the LP₀₁ couplingstrength with all guided modes in the waveguides is nulled, and onecoupling strength between any two higher order modes is substantiallymaximized.
 5. Article according to claim 1, wherein the few-modedwaveguide is three-moded optical fiber, the given guided mode is thefundamental mode LP₀₁ propagating in a forward direction, and n(r), p(r)and θ are selected such that the LP₀₁ to LP₀₁ coupling strength issubstantially nulled, the LP₀₁ to LP₁₁ coupling strength issubstantially nulled, and the LP₀₁ to LP_(02,b) coupling strength issubstantially maximized.
 6. Article according to claim 1, wherein thearticle is a WDM optical fiber communication system that comprises atransmitter, two or more receivers, and optical fiber transmission pathsthat signal-transmissively connect the transmitter and the receivers,wherein at least one of said transmission paths comprises ademultiplexer that comprises said tilted refractive index grating. 7.Article according to claim 6, wherein at least a portion of saidtransmission path is single mode fiber, said single mode fiber beingsignal transmissively connected to said few-moded waveguide.
 8. Articleaccording to claim 1, wherein the few-moded waveguide is a three-modedoptical fiber supporting LP₀₁, LP₁₁ and LP₀₂ modes, and n(r), p(r), andθ are selected to maximize the LP₀₂-LP₁₁ coupling strength and minimizeall other coupling strengths.
 9. Article according to claim 1, whereinall coupling strengths for a given mode are nulled, and wherein onecoupling strength that does not involve said given mode is maximized.10. Article according to claim 1, wherein all coupling strengths exceptone are nulled.
 11. Article according to claim 1, wherein said tiltedrefractive index grating is formed by exposure to UV radiation of afirst wavelength, and is modified by exposure to UV radiation of asecond wavelength, such that a nulling condition of the tiltedrefractive index grating is adjusted.